Abstract:

The velocities and accelerations computation of the navigation satellites is the prerequisite of the velocities and accelerations determination of the receivers. This paper made a systemic analysis of the different methods to calculate the velocities and accelerations of the navigation satellites, including (1) the closed analytical method based on broadcast ephemeris; (2) the numerical differencing method based on position series of the satellite; (3) the analytical differencing method based on position series of the satellite. Firstly, the analytical expressions were deduced based on broadcast ephemeris, three types of broadcast ephemeris, including Kepler elements, GEO, and position-velocity type are discussed. The results can be drawn from precision comparison as follows: (1) The accuracy of velocity and acceleration derived from broadcast ephemeris is relative low, and can not match the high precision applications, such as airborne gravimetric measurement; (2) The acceleration accuracy is higher derived from position-velocity broadcast ephemeris while the Kepler type has higher velocity accuracy; (3) the orbit height is one of the factors of the computation precision. Then, the analytical differencing and numerical differencing based on precision ephemeris to derive velocities and acceleration were analyzed and compared, the results shows that although the analytical method has advantages on efficient, the velocities computation precision is lower for the orbit analytical model built from short term position series is inaccurate, however, the acceleration computation precision compared to the numerical differencing method. In high precision applications, numerical differencing methods should be used for its highest velocity and acceleration computation accuracy. Finally, a static experiment is conducted which data from two CORS (Continues Operational Reference System) stations to evaluate and compare the computation accuracy among the methods mentioned above.

Key words: Key words：velocity, acceleration, accuracy analysis, numerical differencing, analytical differencing, broadcast ephemeris, GNSS